EN

Mathematical Analysis

Emneplan

The course focuses on a broad and rigorous approach necessary to do reliable research within the area of analysis and offers a deeper theoretical understanding that can supplement and be leveraged alongside the knowledge and skills from the previous two specialization courses.

The course provides a perfect basis for any person who wants to venture into this area. It is also a springboard for functional analysis and operator algebras.

A course in analysis at bachelor level is an advantage, preferably with some knowledge of real numbers, cardinality, metric spaces and uniform convergence.

None.

A student who has completed this course should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of this course the student:

  • has basic knowledge of point set topology
  • has basic knowledge of measure theory
  • has basic knowledge of Fourier analysis
  • has basic knowledge of complex function theory

Skills

On successful completion of this course the student:

  • is able to prove some of the most fundamental results of mathematical analysis
  • is able to apply basic notions and results in proofs and derivations

General competence

On successful completion of this course the student:

  • is able to understand literature within these topics
  • can transfer with trust this understanding to own research.
  • General topology, including locally compact Hausdorff spaces
  • Measure theory, including Riesz¿ representation theorem
  • Completeness of Lp spaces, product measures, and complex measures with the Radon- Nikodym theorem
  • Fourier analysis, including the inversion theorem
  • Complex function theory, including the Cauchy- and Liouville theorems, and harmonic functions

Lecturer might exclude or include topics depending on the students attending the course.

Lectures and tutored exercises.

None.

Individual oral exam.

The oral exam cannot be appealed.

None.

Pass/fail.

Two internal examiners. External examiner is used periodically.

Programplan